Shadow mask for a black-stripe color picture tube having successively curved perforations

ABSTRACT

When a shadow mask for a color picture tube of the black-stripe type is extended to coincide with a plane, perforations are formed therethrough parallel to stripes of color luminescent materials in an area adjacent to a center line of the mask extending parallel to the stripes. Perforations placed in remaining areas of the mask, however, are formed along a plurality of curves extending generally parallel to the stripes but having curvatures that grow successively larger with an increase in the distance from the center line.

United States Patent 1191 1111 3, Saito 5] Dec. 9, 1975 SHADOW MASK FOR A BLACK-STRIPE 3,731,129 5/1973 Tsuneta et al. 313/408 COLOR PICTURE TUBE HAVING SUCCESSIVELY CURVED PERFORATIONS Primary ExaminerSiegfried l-I. Grimm [75] Inventor: Yuji Saito Tokyo Japan Attorney, Agent, or Firm-Sughrue, Rothwell, Mion,

Zinn & Macpeak [73] Asslgnee: Nippon Electric Company, Limited,

Tokyo, Japan [57] ABSTRACT [22] Filed: Dec. 10, 1974 When a shadow' mask for a color picture tube of the [21] Appl' 531,414 black-stripe type is extended to coincide with a plane, perforations are formed therethrough parallel to [30] Foreign Appllcatlon Data stripes of color luminescent materials in an area adja- D 0 9 cent to a center line of the mask extending parallel to BC. 1 ,l Japan the Stripes perforations placed in remaining areas of the mask, however, are formed along a plurality of [52] US. Cl 313/403; 354/1 curves extending generally parallel to the stripes but [51] Int. Cl. HOlJ 29/07 having curvatures that grow successively larger with [58] Field of Search 313/403, 402, 407, 408; an increase in the distance from the center line.

6 Cl 11 Dr F' [56] References Cited awmg UNITED STATES PATENTS 3,721,853 3/1973 Naruse et al 313/402 F 2 PRIOR ART I PRIOR ART PRIOR ART U.S. Patent Dec. 9, 1975 Sheet 2 of3 3,925,700

FIG?

US. Patent Dec. 9, 1975 Sheet 3 of3 3,925,700

U UDDDUUU D UDUDUUD U DUUUDUU SHADOW MASK FOR A BLACK-STRIPE COLOR PICTURE TUBE HAVING SUCCESSIVELY CURVED PERFORATIONS BACKGROUND OF THE INVENTION This invention relates to a shadow mask for a color picture tube having color luminescent materials deposited in stripes on an inside surface of a glass face or viewing plate of the picture tube. Preferably, a color picture tube of the type described has black stripes between the respective color luminescent stripes. A shadow mask according to this invention is therefore described herein with regard to a color picture tube of the so-called black-stripe type although the shadow mask is not restricted to that for use in a picture tube of the last-mentioned type.

In the manner known in the art, each color picture tube includes a shadow mask at present. The shadow mask does not only serve to reproduce a colored picture but also is resorted to on depositing the color luminescent materials on the face plate inside surface. A conventional shadow mask for a color picture tube of the type described is of a general shape of a rectangle and has a plurality of perforations which are elongate in the direction of the minor or shorter sides of the rectangle and arranged in a regular array with respect to the minor sides and to major or longer sides of the rectangle. With this shadow mask, the color luminescent material stripes become distorted at peripheral portions of the mask to result in colored pictures of an unpleasing appearance. Although it has been proposed to resort to partial exposure in the manner later described with reference to the accompanying drawing, this reduces the productivity of color picture tubes.

SUMMARY OF THE INVENTION It is therefore an object of the present invention to provide a shadow mask for a color picture tube of the type described, capable of affording agreeable colored pictures.

It is another object of this invention to provide a shadow mask of the type described, with which a color picture tube can be produced with excellent efficiency.

A color picture tube of the type described has a generally rectangular glass face plate of a substantially spherical curvature. A shadow mask for the color picture tube has a shape of a similar rectangle and an approximately equal spherical curvature so as to be positioned substantially parallel to an inside surface of the face plate and has a plurality of perforations formed therethrough. The perforations are elongate in the direction of a predetermined pair of sides of the similar rectangle and arranged in a regular array with respect to the direction and another direction perpendicular to the first-mentioned direction. According to this invention, the perforations are arranged, when the mask is extended to coincide with a plane, parallel to the above-mentioned pair of sides in an area adjacent to a center line bisecting the remaining pair of the sides and, in remaining areas of the mask, along a plurality of curves whose curvatures grow larger with an increase in the distance from the center line.

BRIEF DESCRIPTION OF THE DRAWING FIG. 1 is a fragmentary perspective view of a glass panel of a color picture tube, a shadow mask therefor, and a conventional device for projecting light rays onto an inside surface of the panel through perforations of a conventional shadow mask;

FIG. 2 is a perspective view of a conventional shadow mask;

FIG. 3 shows a back view of the panel together with several stripes of light rays projected onto the inside or back surface of the panel through perforations of a conventional shadow mask;

FIG. 4 shows a back view of the panel and a restricted area for the light rays;

FIG. 5 illustrates an arrangement of perforations of a shadow mask according to the instant invention;

FIG. 6 is a schematic perspective view of a shadow mask for describing the arrangement of perforations with reference to an orthogonal coordinate system;

FIG. 7 shows a projection of the perforations on the X-Y plane of the coordinate system;

FIG. 8 again shows the coordinate system illustrated in FIG. 6 for describing an arrangement of the perforations of a prototype of the shadow masks according to this invention;

FIG. 9 shows the prototype extended on a plane, together with the X and Y axes of the coordinate system projected onto the plane;

FIG. 10 shows another orthogonal coordinate system for describing a simplified arrangement of the perforations of the prototype; and

FIG. 11 is an exploded schematic perspective view of an arrangement for manufacturing shadow masks according to this invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS Referring to FIGS. 1 and 2, a color picture tube of the black-stripe type has a glass member generally called a glass panel in the art. The panel consists of a generally rectangular glass face or viewing plate 20 of a substantially spherical curvature and a skirt portion extended from the periphery of the face plate 20 generally perpendicularly therof. A shadow mask 21 for the color picture tube has a surface of a similar rectangle and an approximately equal spherical curvature so as to be positioned substantially parallel to an inside or back surface of the face plate 20 and has a plurality of perforations 22 formed through the mask surface. The perforations 22 are elongate in the direction of minor or shorter sides of the rectangle and arranged in a regular array with respect to the minor sides and to major or longer sides of the rectangle. At a first stage of manufacture, the shadow mask 21 is flat. The perforations 22 are formed through the flast mask plate parallel to the minor sides. The slotted mask plate is subsequently pressed into a shadow mask 21 having a surface of a substantially spherical curvature. The stripes of color luminescent materials are deposited on the face plate inside surface by coating at first the inside surface with a photosensitive film (not shown), on which a beam of light rays is projected through the perforations 22 from a light source 25 placed at a point where electron source means (not shown) of the color picture tube is subsequently positioned. It is to be noted here that the perforations 22 arranged along a line substantially parallel to the minor sides are partitioned by a plurality of bridges 26. It is therefore necessary that the light source 25 be elongate in the direction of the minor sides and that the length be longer than the perforations 22.

* Referring also to FIGS. 3 and 4, stripes S of the light projected on the face plate inside surface become distorted with an increase in the distance from the center point of the face plate 20. As a result, stripes (not shown) of the color luminescent materials and black stripes (not shown) disposed between the respective color luminescent stripes are deposited on the face plate inside surface accordingly distorted. This results, in turn, in colored pictures of an objectionable appearance. This undesirable tendency becomes more serious in wider deflection-angle picture tubes. In order to obviate the distiortion of the stripes S of light and consequently the color luminescent and black stripes, it has been proposed to mount the light source 25 on a device 27 for rocking the light source 25 in the manner later described. The device 27 has a slotted plate 28 for moving an area 29 exposed to the light rays parallel to the minor sides in synchronism with the rocking movemento f the light source 25. It is, however, impossible with the partial exposure as called herein to utilize the whole rays emitted by the light source 25. This reduces the productivity of the color picture tubes.

Referring to FIGS. 5 and 6, a shadow mask 21 according to the present invention has perforations 22 formed, before the mask surface is pressed into a substantially spherical form, parallel to the minor sides in an area adjacent to a center line bisecting the major sides of the rectangle and, in remaining areas of the mask surface, along a plurality of curves whose. curvatures grow larger with an increase in the distance from the center line. It is now presumed that the shadow mask 21 has a spherical surface having its center of curvature at a point 30 and that the elongate light source 25 is placed at an origin of a right-handed orthogonal coordinate system having an X and a Y axis parallel to the major andminor sides of the mask 21 and a Z axis perpendicular to the X-Y plane. The light beam emitted by the source 25 along a plane 31 that passes through the Y axis and makes an angle a with respect to the Z axis intersects the mask surface along a small circle .32. Specifically stated, the perforations 22 (not shown in FIG. 6) of a shadow mask 21 according to this invention are arranged along the small circle 32 and similar small circles. On the other hand, the perforations 22 (not shown in FIG. 6) of a conventional shadow mask are arranged along great circles exemplified at 33 as an intersection of the mask surface and a plane 34 that is parallel to the Y axis and makes an angle [3 with respect to the Z axis. If the planes 31 and 34 have acornmon point 35 on the mask surface, the angles are given by:

where R represents the radius of the spherical surface, and the planes 31 and 34:

z (Z/X)x (4) and z=([Z+m]/X)x-m, respectively.

Referring further to FIG. 7, an angle (b measured from a plane 36 parallel to the X-Z plane and passing through the common point 35 to that portion of the small circle 32 which is adjacent to the common point 35 is:

p,=arctan([X+ l) (6) from Equations (3) and (4). A similar angle for the from Equations (3) and (5). In Equations (6) and (7), Y represents the Y coordinate of the common point 35. The angles (1) and are not equal to each other except for perforations 22 placed on the X-Z and Y-Z planes. It is now understood that the stripe portions S formed on the face plate inside surface by the light beams projected along the plane 31 and similar planes depicted by dashed lines and passing through the perforations 22 arranged on the great circle 33 become as indicated by hatched areas if it is surmised that the face plate inside surface is in contact with the mask'surface for mere simplicity of illustration.

Referring again to FIGS. 1 and 4 and also to FIG. 7, the device 27 rocks the light source 25 so that the plane along which the light rays are projected may make an angle (1) to the X-Z plane at a pointplaced in the moving area 29 for the partial exposure. In contrast, the perforations 22 of a shadow mask 21 according to this invention are arranged as described along the small circles, such as 32. The stripe portions of the light rays projected on the face plate inside surface are therefore aligned, for example, on the small circle 32 if it is again surmised that the faace plate inside surface is in direct contact with the mask surface. It is consequently unnecessary to resort to the device 27 thus far described on depositing the color luminescent and black stripes. This not only raises the productivity of the color picture tubes of the type described but also raises the precision of the stripe arrangement. In addition, this invention reduces the cost of installation for manufacture of the color picture tubes of the type described.

Referring to FIGS. 8 and 9, a shadow mask is generally manufactured by the use of a flat prototype of patterns for the perforations to be formed through the mask surface. It is therefore an important task to form a prototype for shadow masks according to this invention. In FIG. 8, one of the small circles 32 along which the perforations should be aligned according to this invention intersects the X-Z plane at a point 36. Let the Z axis intersect the spherical surface of the shadow mask at a point 40 and the distance on the spherical surface between the point 36 and 40 be denoted by L. When the shadow mask is not yet pressed into the spherical surface, or when the mask were extended to coincide with a plane, a great circle 41 that passes through the point 36 be comes a straight line 41 which, as illustrated in FIG. 9, is parallel to a Y axis and passes through a point 36 spaced L along an X axis from an origin coincident with the-point 40. The point 36 is a point which the point 36 illustrated with reference to FIG. 8 assumes on the flat or extended shadow mask surface. The X and Y axes of FIg. 9 are orthogonal projections of the X and Y axes of FIG. 8 on the flat prototype surface. That portion of the small circle 32 of alignment of the perforations according to this invention which is adjacent to the great circle 41 may approximately be represented by a curve of intersection 42 of a plane 43 (not shown in FIGS. 8 and 9) including the small circle 32 and a right cylindrical surface 44 (not shown in FIGS. 8 and 9) which is tangential to the spherical surface at the great circle 41, namely, which has the great circle 41 as the director curve. The perfo- -rations are now-jaligned according to this invention along the curve or an ellipse of approximation 42 instead of the small circle 32. When the shadow mask is extended as described, the ellipse of approximation 42 becomes a curve 42', which may be specified by the distances, such as PP, from the straight line 41 and the ordinates of the line segments representative of the distances.

Referring to FIG. in addition, another righthanded orthogonal XYZ coordinate system is introduced in order to facilitate calculation of the distances in question. The X-Y plane includes the great circle 41, the origin being placed at the center of the great circle 41. The point 36 is on the X axis in its positive region, the coordinates of the point 36 being given by (R, 0, 0). The plane 43 of the small circle 32 and the ellipse of approximation 42 is depicted. The cylindrical surface 44 and the distance PP are also illustrated In FIG. 8, let the coordinates of the point 36 be (X, 0, Z) although the values of X and Z may differ from those for the point 35 illustrated with reference to FIG. 6. If again written by a and B, respectively, the angles made by the plane 43 and another plane including the great circle 41 to the Z axis are given by Equations (1) and (2). An angle (1) between these planes is given, in terms of X, by:

when the relation X Z R for the point 36 is taken into consideration. Alternatively,

tand) m-sin(L/R)/[R m'cos(L/R)] (8) because [3 L/R. In FIG. 10, the angle measured from the X axis to the plane 43 is (1). Therefore,

z'=tan 4x '+Rtan 4) gives the plane 43. Furthermore,

PP Iamp'X Rtanzb, (9) where X represents the current X coordinate of the point P placed on the great circle 41. In FIG. 9, the abscissa X of the point P is:

X L tanda-X R'tand) because X L PP. The ordinate Y of the point P is equal to the ordinate of the point P and, hence, the arc between the points 36 and P of the great circle 41 depicted in FIG. 10. Therefore:

Y Rarcsin( Y/R), where Y represents the current I coordinate of the point P. Inasmuch as x" Y R2, the curve of approximation 42' along which the perforations should be aligned in accordance with this invention is:

x R-tandz L) /(R 'tan sin Y/R) 1, 10 where tand: is given by Equation (8) and L is given by:

Referring to FIGS. 5, 9, and 10, the curves of approximation, such as 42, will now be specified in a more practical form. Let the horizontal and vertical pitches of the perforations 22 in a flat prototype be denoted by H and V. In addition, let the point P be a center point of the (i,j)-th one of the perforations 22, i being counted horizontally from the perforations aligned along the vertical center line of the flat prototype and j being counted vertically from every other perforation aligned on the horizontal center line. The abscissa L of the point 36 and the ordinate Y of the point P are equal to iH and jV. Inasmuch as the are between the points 36 and P of the great circle 41 is equal to Y as described, X is equal to R'cos(Y/R) in FIG. 10. Therefore:

PP Rll cos( Y/Rlltanrb results from Equation (9). This applies also to the substantially vertically aligned perforations, two of which are placed contiguous to the horizontal center line,

when jV is deemed to represent the current Y coordinate for the curves of alignment of these perforations. After all, the distance to or a small displacement PPA (iii), from a straight line 41' defined by X iH, for the (i,j)-th perforation is:

PP'(i,j) R[l cos(iV/R)]tand mR[l cos(iV/R)]sin(iH/R)/[R m'cos(iH/R)]. (l I) For example, the radius of curvature R of a shadow mask surface be 800 mm. The distance m between the center of curvature 30 and the light source 25 be 535 mm. The pitches H and V be 0.52 mm and 1.00 mm, respectively. Now, the small displacement PP for the (364,j)-th perforation is:

PP(364..i)=385.25[Icos(0.07l6j)l, (12 when the argument of the cosine is given in degrees.

It will now be discussed to what extent the small circles, such as 32, depicted in FIGS. 6 and 8 are approximated within the effective or practical area of a prototype or a shadow mask according to this invention by Equation (10), (1 l), or (12) for the curves, such as 42, on a plane. At first, it should be understood that the error introduced on pressing a flat shadow mask into a spherical form is only of the order of a score of microns and negligible in practice. In the next place, the error 8X introduced by substitution of an ellipse 42 depicted in FIGS. 8 and 10 for the small circle 32 is, from the fact that both curves 32 and 42 lie on a common plane 43:

5X p R-arctan(p/ where p represents the maximum value within the ef fective area of the distance between a great circle, such as 41, and an ellipse of approximation, such as 42, along the generating line of a cylindrical surface, such as 44. For the effective area, L and Y may be at most equal to 190 mm and mm, respectively. The distance p becomes a maximum when L mm and Y 140 mm, where the abscissa X of the curve 42 becomes 184.49 mm. Hence, the maximum distance p is 5.51 mm. With these values, the absolute value of 8X is equal to 0.01 mm at most. It is now understood that the latter error is also negligible in practice.

A shadow mask may often have different radii of curvature in the X-Z and Y-Z planes of FIG. 8. For example, let arcs of a first and a second circle of radii R and R be drawn on the X-Z and Y-Z planes, both having the centers on the Z axis and passing through the point or vertex 40, and let a plane on which the second arc is present be tilted from the Y-Z plane with the center of the first circle fixed and with the second arc guided by the first arc to generate a substantially spherical surface of a shadow mask. If the center of the first circle is placed at a point 30 whose coordinates are (0, 0, m), the angle 4) is given by:

b -sin(L/R,.)/[ R, m-cos(L/R,.)] with reference to Equation (8). Inasmuch as the curve 41 is a circle of radius R the curve of approximation 42 is an ellipse defined by the intersection of the plane 43 and a cylindrical surface of radius R,,. Therefore, Equations (10) and (11) become:

For example, the small displacement for the (364,j)- th perforation of a flat prototype for shadow masks of Incidentally, the small displacements for the 364,l20)-th and (364,127)-th perforations are 4.17 and 4.67 mm according to Equation (12). The corresponding displacements are 4.01 and 4.51 mm according to Equation (12). The difference in the displacements is 0.5 mm in both cases. This shows that the perforation arrangement for a spherical shadow mask may be substituted for that for a substantially spherical one in practice.

Referring again to FIG. 5, a shadow mask of the color picture tube of the type described generally has curved minor sides. In a conventional shadow mask, several lines of the perforation arrangement are cut short in longitudinal end portions of the mask. This results in an additionally unpleasing appearance of the colored pictures at the horizontal end portions. A shadow mask naturally has rounded corners. Let a point of connection between the minor side and a rounded corner be placed at a point whose X and Y coordinates are (X Y,). The abscissa is:

X.=(X .R..) M where R, and X represent the radius of curvature of the curved minor side and the abscissa of an intersection of the X axis and the curved minor side. In a shadow mask for a color picture tube of the type described, X 185.77 mm when R 2300 mm and Y 127V. If X 364I-I, the abscissa X of the (364,127)-th perforation is:

x, 364 x 0.52 PP'(364,I27) 185.25 mm according to Equation (12 The difference between X s and X is only 0.52 mm. It is therefore possible to shape the minor sides of a shadow mask according to this invention along the longitudinally outermost lines of perforation arrangement.

Finally referring to FIG. 11, a shadow mask according to this invention may be manufactured by the use of a flat prototype 50 through which substantially vertically running slits 51 are formed in the manner thus far described and a transparent screen 52 on which opaque line segments 53 are printed or otherwise formed so as to intersect the slits 51 at portions corresponding to the bridges 26 of a flat shadow mask. The prototype 51 and screen 52 are superposed on a metal plate 55 coated with a photosensitive film, which is exposed to a light source exemplified by an incandescent lamp 56 through'the slits 51 cut at portions by the opaque line segments 53. The slits 51 may be readily formed by the use ofa numerically controlled machine. In this connection, it should be mentioned that the precision for the line segments 53 is not serious because the color luminescent stripes and the black stripes, if any, are continuous along the curves mentioned above.

What is claimed is:

1. In a shadow mask for a color picture tube having a generally rectangular glass face plate of a substantially spherical curvature, and mask having a shape of a similar rectangle and an approximately equal spherical curvature to be positioned substantially parallel to an inside surface of said face plate and having a'plurality of perforations formed therethrough, said perforations being elongate in a first direction parallel to a predetermined pair of sides of said similar rectangle and arranged in a regular array with respect to said direction and to a second direction perpendicular to said first direction, the improvement wherein said perforations are arranged, when said mask is extended to coincide with a plane, parallel to said first direction in an area adjacent to a center line bisecting the remaining pair of said sides and, in remaining areas of said mask, along a plurality of curves whose curvatures grow successively larger with an increase in the distance from said center line.

2. A shadow mask according to claim 1, wherein said predetermined side pair runs along those two of said curves which are disposed outermost as regards said second direction.

3. A shadow mask according to claim 1, said picture tube including electron source means for projecting electrons onto said face plate inside surface through said mask, said approximately equal spherical curvature being R, in an X-Z plane and-R in a Y-Z plane, said X-Z and Y-Z planes being coordinate planes of an orthogonal XYZ coordinate system having an X and a Y axis in said second and first directions and a Z axis passing through a center point of said mask, centers of curvature for the curvatures R anad R being placed on said Z axis, wherein, when said mask is extended to coincide with a plane, said perforations are arranged with a pitch of H along said X-Z plane and a pitch of V in said first direction and said curves are specified by small displacements towards said center line from respective straight lines passing through points aligned along said X-Z plane at X-coordinate of iI-I (i being representative of 0 and positive and negative integers), said displacements at Y-coordinates of V (i being representative of 0 and positive and negative integers) being given by:

where m represents the distance between said electron source means and said center of curvature for the curvature R 4. A shadow mask according to claim 3, wherein said predetermined side pair runs along those two of said curves which are disposed outermost as regards said second direction.

5. A shadow mask according to claim 3, wherein R and R,, are equal to each other and said displacements are given by:

mR[l cosUV/R)]sin(iH/R)/[R m'cos(iH/R)], where R represents the equal curvature R, or R and m represents the distance between said electron source means and the center of curvature for said equal curvature.

6. A shadow mask according to claim 5, wherein said predetermined side pair runs along those two of said curves which are disposed outermost as regards said second direction.

UNITED STATES PATENT AND TRADEMARK OFFICE CERTIFICATE OF CORRECTION PATENT NO. 3,925,700

DATED December 9, 1975 INV ENTOR(S) Yuji Saito It is certified that error appears in the ab0ve-identified patent and that said Letters Patent are hereby corrected as shown below:

IN THE SPECIFICATION:

Column 2, line 41, delete "therof". and insert thereof Column 4, line 4, delete and insert line 28, delete "faace" and insert face line 57, delete "FIg. and insert FIG.

Column 6, line 3, delete PP' l1. and insert line 67, before "364", insert Column 7, line 10, delete "in" and insert at IN THE CLAIMS:

Column 7, line 53, before "mask", delete "and" and insert said Column 8, line 25, delete "anad" and insert and Signed and Scaled this n n h Day of March 1976 [SEAL] Attest:

RUTH C. MASON Arresting Officer C. MARSHALL DANN Commissioner ofParents and Trademarks UNITED STATES PATENT AND TRADEMARK OFFICE CERTIFICATE OF CORRECTION PATENT NO. 3,925,700 9 DATED December 9, 1975 |NV ENTOR(S) Yuji Saito It is certified that error appears in the above-identified patent and that said Letters Patent are hereby corrected as shown below: C

IN THE SPECIFICATION:

Column 2, line 41, delete "therof"v and insert thereof O Column 4, line 4, delete "(1 and insert line 28, delete "faace" and insert face Q line 57, delete "FIg." and insert FIG.

Column 6, line 3, delete "PP' A. and insert Q line 67, before "364", insert Column 7, line 10, delete "in" and insert at IN THE CLAIMS:

Column 7, line 53, before "mask", delete "'and" and insert.

-- said Column 8, line 25, delete "anad" and insert and Signed and Scaled this ninth D y Of March 1976 [SEAL] O Attest.

RUTH C. MASON C. MARSHALL DANN Arresting Ojjrcer (ommixsiuner u/Parenls and Trademarks 

1. In a shadow mask for a color picture tube having a generally rectangular glass face plate of a substantially spherical curvature, and mask having a shape of a similar rectangle and an approximately equal spherical curvature to be positioned substantially parallel to an inside surface of said face plate and having a plurality of perforations formed therethrough, said perforations being elongate in a first direction parallel to a predetermined pair of sides of said similar rectangle and arranged in a regular array with respect to said direction and to a second direction perpendicular to said first direction, the improvement wherein said perforations are arranged, when said mask is extended to coincide with a plane, parallel to said first direction in an area adjacent to a center line bisecting the remaining pair of said sides and, in remaining areas of said mask, along a plurality of curves whose curvatures grow successively larger with an increase in the distance from said center line.
 2. A shadow mask according to claim 1, wherein said predetermined side pair runs along those two of said curves which are disposed outermost as regards said second direction.
 3. A shadow mask according to claim 1, said picture tube including electron source means for projecting electrons onto said faCe plate inside surface through said mask, said approximately equal spherical curvature being Rx in an X-Z plane and Ry in a Y-Z plane, said X-Z and Y-Z planes being coordinate planes of an orthogonal XYZ coordinate system having an X and a Y axis in said second and first directions and a Z axis passing through a center point of said mask, centers of curvature for the curvatures Rx anad Ry being placed on said Z axis, wherein, when said mask is extended to coincide with a plane, said perforations are arranged with a pitch of H along said X-Z plane and a pitch of V in said first direction and said curves are specified by small displacements towards said center line from respective straight lines passing through points aligned along said X-Z plane at X-coordinate of iH (i being representative of 0 and positive and negative integers), said displacements at Y-coordinates of jV (j being representative of 0 and positive and negative integers) being given by: mRy(1 -cos(jV/Ry))sin(iH/Rx)/(Rx - m.cos(iH/Rx)), where m represents the distance between said electron source means and said center of curvature for the curvature Rx.
 4. A shadow mask according to claim 3, wherein said predetermined side pair runs along those two of said curves which are disposed outermost as regards said second direction.
 5. A shadow mask according to claim 3, wherein Rx and Ry are equal to each other and said displacements are given by: mR(1 -cos(jV/R))sin(iH/R)/(R - m.cos(iH/R)), where R represents the equal curvature Rx or Ry and m represents the distance between said electron source means and the center of curvature for said equal curvature.
 6. A shadow mask according to claim 5, wherein said predetermined side pair runs along those two of said curves which are disposed outermost as regards said second direction. 